Light scattering in a spatially-correlated particle field: Role of the radial distribution function

Abstract

Radiative transfer through particle-laden media such as clouds can be impacted by variations in particle spatial distributions. Due to mixing and inertial effects of droplets suspended in the almost always turbulent atmosphere, cloud particles are often spatially-correlated. The correlations result in clusters and voids within the droplet field that, even when smaller than the photon mean free path, can lead to deviations from the exponential extinction law. Prior work has numerically investigated these departures from exponential attenuation in absorptive media; this work extends those results for a scattering medium. The problem is explored with a Monte Carlo Ray Tracing (MCRT) program capable of tracking light attenuation through both perfectly random (uncorrelated) and spatially correlated collections of scatterers and/or absorbers. The MCRT program is favorably compared to two-stream flux equations, and numerical exploration of the pure-absorption case is used to determine the sampling statistics necessary to characterize radiative transmission within the numerical simulation. Light transmission through fields of spatially-correlated, non-absorbing, scattering particles is explored. Particles are distributed following a Matérn Point Process, which allows cluster strength and size, as well as the usual variables of particle scattering cross section and number density to be varied. The results show that the degree of non-exponential attenuation is determined by the magnitude and shape of the radial distribution function, which describes correlations in discrete (non-continuous) particle distributions. Parametric studies revealed that the number of clusters and cluster radius, factors in the Matérn radial distribution function, impact direct, diffuse and backward radiative transfer. The Matérn RDF is shown to be consistent with a previous “cloudlet” approach, providing a bridge between the analytical cloudlet model and continuous correlation function approaches.